(Answer Key) Answer Key
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Name 
Date Class 

10-2 
Reteach 

Solving Multistep Equations 

5 
m1055 

2x2 
22

LESSON 
To combine like terms, add (or subtract) coefficients. 

2m  3m  (2  3)m  5mx  3x  (1  3)x  2x 

To solve an equation that contains like terms, first combine the like terms. 

2m  3m  35  25 Check: Substitute into the original. 
5m  10 Combine like terms. 2m  3m  35  25 

Divide by 5. 
2(2)  3(2)  35  25 

m  24  6  10 
10  10  

x  6  3x  5  13 Check: x  6  3x  5  13 
2x  11  13 Combine like terms. 1  6 3(1)  5  13 
11 11 Subtract 11. 1  6  3  5  13 
2x  2 1  14  13 

Divide by 2. 
13  13  

x  1 

Complete to solve and check each equation. 

1. 4z  7z  20 1 Check: 4z  7z  20  1 
z  Combine like terms. 4( )  7( )  20  1 
z 
 
Divide.   

z  

2. t  1  4t  8  21 Check: t  1  4t  8  21 
t  Combine like terms.  1  4( )  8  
Subtract.  1  8  21 
t   21 

t

 Divide. 
t  

Copyright  by Holt, Rinehart and Winston. 

21 
Holt Middle School Math

All rights reserved. 


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Name Date Class 

10-2 
Reteach 

Solving Multistep Equations (continued) 

123 
555

LESSON 


111 
42211121
42442

112
10


21 


42


2

11 

26


11 
2622

2

mm 5 

342

When you add fractions, the result is a fraction.

When fractions are in an equation, you can clear the fractions immediately. 

Check:

x  3  

The LCD of 4 and 2 is 4. 

1

 (10)  3 

4

4 


x  4  3  4

Multiply every term by LCD.

x  12  2 The fractions are cleared.

12 Subtract 12.
1 

2

x  10 

Complete to solve and check. 

3.
1

 t  2 Determine the LCD. Check:

6

() . 


()  2


1

 t 

2







 2 Multiply every term by LCD.
 2


t  

t  

The fractions are cleared.

 2


t  t  

t  Combine like terms. 

t

 Divide. 
t  

m 5 
42

m  m  The fractions are cleared. 
m  Combine like terms. 
Add. 

m  

m 

34

m


3

4.
 1 . 


Determine the LCD. 







1  


Multiply every term by the LCD. 

 Divide. 
Check:

 1 .


m  

5 
2

      

12121212

Copyright  by Holt, Rinehart and Winston. 

22 Holt Middle School Math

All rights reserved. 


Copyright  by Holt, Rinehart and Winston. 19 Holt Middle School MathAll rights reserved. 
Practice B 
Solving Multistep Equations10-2 
LESSON 
Solve. 
1. 2x 5x 4 25 2. 9 3y 2y 14 3. 16 4w 2w 2 
4. 26 3b 2 7b 5. 31 4t t 40 6. 14 2x 4x 20 
7.
5 
8
m 
3 
5

3 
8
m 
2 
5
8. 29.2 9. 7a 16 3a 7 
1.7n 5.8 5.3n  11 
10.
1 
2
x 1 
3 
4
x 9 11. 7.5m 3 3.5m 15 12.
2 
5
x 3 
4 
5
x 
1 
5
 
13. 7k 12 4.5k 18 14. 6y 9 4y 3 15. 5a 1 a 11 
16. The measure of an angle is 28 greater than its complement. 
Find the measure of each angle. 
angle 59; complement 31 
17. The measure of an angle is 21 more than twice its supplement. 
Find the measure of each angle. 
angle 127; supplement 53 
a 2y 6k 12 
x 7m 4.5x 8 
a 5n 5m 1 
x 3t 3b 7 
w 3y 5x 3 
18. The perimeter of the triangle is 126. 
Find the measure of each side. 
AC 25; BC 50; AB 51 
19. The base angles of an isosceles 
triangle are congruent. If the 
measure of each of the base 
angles is twice the measure of the 
third angle, find the measure of all 
three angles. 
36; 72; 72 
A 
C B 
2x1 
2x 
x 
Copyright  by Holt, Rinehart and Winston. 20 Holt Middle School MathAll rights reserved. 
Practice C 
Solving Multistep Equations10-2 
LESSON 
Solve and check. 
1. 54 8x 7x 21 2.
2 
3
y 27 
3 
4
y 24 3. 18x 21 15x 3 
4. 1.15a 8 0.4a 7 5. 3 13w 9w 8 6.
4 
9
m 13 
1 
3
m 4 
7. 182d 3.5 20d 19.7 8.
3 
4
k 28 
2 
3
k 37 9.
3 
4 
x
2 
3 
x
2 
5
 
10. Takeo and Manuel drove to a baseball game together. The 
tickets cost $10.50 each and parking was $6. Popcorn cost 
$2.25 a box and each of the boys bought a box of popcorn. 
Takeo bought 1 drink and Manuel bought 2 drinks. The baseball 
game and the snacks cost the boys a total of $39.75. How much 
did each of the drinks cost? 
$2.75 
x 4
4 
5k 780d 0.1 
m 81w 
1 
4 
1
or 2
3 
4 a 20 
x 8y 36x 2.2 
11. The perimeter of right triangle ABC is 
132. Find the length of the 
hypotenuse. 
61 
12. Mrs. Lincoln budgets her monthly take-home pay. The remainder 
she deposits in her savings account. She budgets 
1 
3
of her 
take-home pay for rent, 
1 
8
for car expenses, 
1 
6
for food, 
2 
1 
4
for 
insurance and 
1 
1 
6
for entertainment. What is Mrs. Lincolns 
monthly take-home pay if she deposits $546 in her savings 
account? 
$2016 
A 
C B 
4x17 
5x5 
x 
Copyright  by Holt, Rinehart and Winston. 21 Holt Middle School MathAll rights reserved. 
Reteach 
Solving Multistep Equations10-2 
LESSON 
To combine like terms, add (or subtract) coefficients. 
2m 3m (2 3)m 5m x 3x (1 3)x  2x 
To solve an equation that contains like terms, first combine the like terms. 
2m 3m 35 25 Check: Substitute into the original. 
5m 10 Combine like terms. 2m 3m 35 25 

5 
5 
m

15 
0
Divide by 5. 2(2) 3(2)  35 25 
m 2 4 6  10 
10 10  
x 6 3x 5 13 Check: x 6 3x 5 13 
2x 11 13 Combine like terms. 1 6 3(1) 5  13 
11 11 Subtract 11. 1 6 3 5  13 
2x  2 1 14  13 
 
 
2 
2 
x 
 
2 
2
Divide by 2. 13 13  
x  1 
Complete to solve and check each equation. 
1. 4z 7z  20 1 Check: 4z 7z  20 1 
z  Combine like terms. 4( ) 7( )  20 1 
 
 
3 
3 
z Divide.   
z  
2. t 1 4t 8 21 Check: t 1 4t 8 21 
t  Combine like terms. 1 4( ) 8  
9 9 Subtract. 1  8  21 
t    21 
 
 
3 
3 
t Divide. 
t  4 
Copyright  by Holt, Rinehart and Winston. 19 Holt Middle School MathAll rights reserved. 
Practice B 
Solving Multistep Equations10-2 
LESSON 
Solve. 
1. 2x 5x 4 25 2. 9 3y 2y 14 3. 16 4w 2w 2 
4. 26 3b 2 7b 5. 31 4t t 40 6. 14 2x 4x 20 
7.
5 
8
m 
3 
5

3 
8
m 
2 
5
8. 29.2 9. 7a 16 3a 7 
1.7n 5.8 5.3n  11 
10.
1 
2
x 1 
3 
4
x 9 11. 7.5m 3 3.5m 15 12.
2 
5
x 3 
4 
5
x 
1 
5
 
13. 7k 12 4.5k 18 14. 6y 9 4y 3 15. 5a 1 a 11 
16. The measure of an angle is 28 greater than its complement. 
Find the measure of each angle. 
angle 59; complement 31 
17. The measure of an angle is 21 more than twice its supplement. 
Find the measure of each angle. 
angle 127; supplement 53 
a 2y 6k 12 
x 7m 4.5x 8 
a 5n 5m 1 
x 3t 3b 7 
w 3y 5x 3 
18. The perimeter of the triangle is 126. 
Find the measure of each side. 
AC 25; BC 50; AB 51 
19. The base angles of an isosceles 
triangle are congruent. If the 
measure of each of the base 
angles is twice the measure of the 
third angle, find the measure of all 
three angles. 
36; 72; 72 
A 
C B 
2x1 
2x 
x 
Copyright  by Holt, Rinehart and Winston. 20 Holt Middle School MathAll rights reserved. 
Practice C 
Solving Multistep Equations10-2 
LESSON 
Solve and check. 
1. 54 8x 7x 21 2.
2 
3
y 27 
3 
4
y 24 3. 18x 21 15x 3 
4. 1.15a 8 0.4a 7 5. 3 13w 9w 8 6.
4 
9
m 13 
1 
3
m 4 
7. 182d 3.5 20d 19.7 8.
3 
4
k 28 
2 
3
k 37 9.
3 
4 
x
2 
3 
x
2 
5
 
10. Takeo and Manuel drove to a baseball game together. The 
tickets cost $10.50 each and parking was $6. Popcorn cost 
$2.25 a box and each of the boys bought a box of popcorn. 
Takeo bought 1 drink and Manuel bought 2 drinks. The baseball 
game and the snacks cost the boys a total of $39.75. How much 
did each of the drinks cost? 
$2.75 
x 4
4 
5k 780d 0.1 
m 81w 
1 
4 
1
or 2
3 
4 a 20 
x 8y 36x 2.2 
11. The perimeter of right triangle ABC is 
132. Find the length of the 
hypotenuse. 
61 
12. Mrs. Lincoln budgets her monthly take-home pay. The remainder 
she deposits in her savings account. She budgets 
1 
3
of her 
take-home pay for rent, 
1 
8
for car expenses, 
1 
6
for food, 
2 
1 
4
for 
insurance and 
1 
1 
6
for entertainment. What is Mrs. Lincolns 
monthly take-home pay if she deposits $546 in her savings 
account? 
$2016 
A 
C B 
4x17 
5x5 
x 
Copyright  by Holt, Rinehart and Winston. 21 Holt Middle School MathAll rights reserved. 
Reteach 
Solving Multistep Equations10-2 
LESSON 
To combine like terms, add (or subtract) coefficients. 
2m 3m (2 3)m 5m x 3x (1 3)x  2x 
To solve an equation that contains like terms, first combine the like terms. 
2m 3m 35 25 Check: Substitute into the original. 
5m 10 Combine like terms. 2m 3m 35 25 

5 
5 
m

15 
0
Divide by 5. 2(2) 3(2)  35 25 
m 2 4 6  10 
10 10  
x 6 3x 5 13 Check: x 6 3x 5 13 
2x 11 13 Combine like terms. 1 6 3(1) 5  13 
11 11 Subtract 11. 1 6 3 5  13 
2x  2 1 14  13 
 
 
2 
2 
x 
 
2 
2
Divide by 2. 13 13  
x  1 
Complete to solve and check each equation. 
1. 4z 7z  20 1 Check: 4z 7z  20 1 
z  Combine like terms. 4( ) 7( )  20 1 
 
 
3 
3 
z Divide.   
z  
2. t 1 4t 8 21 Check: t 1 4t 8 21 
t  Combine like terms. 1 4( ) 8  
9 9 Subtract. 1  8  21 
t    21 
 
 
3 
3 
t Divide. 
t  4 
(<< Back <<) << Back <<
21 21  
 
 
12 
3 
254123 
164 
21442193 
21 21 7 
214928 
 
2 
3 
1
 
77213 
Copyright  by Holt, Rinehart and Winston. 22 Holt Middle School MathAll rights reserved. 
Reteach 
Solving Multistep Equations (continued) 10-2 
LESSON 
When you add fractions, the result is a fraction.
1 
5

2 
5

3 
5
 
When fractions are in an equation, you can clear the fractions immediately. 

1 
4
x 3 
1 
2
The LCD of 4 and 2 is 4. Check:
1 
4
 (10) 3 
1 
2
 
4 
1 
4
x 4  3 4
1 
2
Multiply every term by LCD. 
4 
10
 
1 
4 
2
1 
2
 
x 12 2 The fractions are cleared.
2 
4

1 
2
 
12 12 Subtract 12.
1 
2

1 
2
  
x  10 
Complete to solve and check. 
3.
1 
2
 t 
1 
6
 t 2 Determine the LCD. Check:
1 
2
( ) 
1 
6
( )  2 

1 
2
t  
1 
6
t   2 Multiply every term by LCD.
2 
3

2 
1
 2 
t t  The fractions are cleared.
2 
4
 2 
t  Combine like terms. 

4 
4 
t Divide. 
t  
4.
m 
3

m 
4
1 
5 
2
Determine the LCD. 

m 
3
 
m 
4
 1  
5 
2
Multiply every term by the LCD. 
m  m   The fractions are cleared. 
  Combine like terms. 
12 12 Add. 
m  

7 
7 
m
 Divide. 
m  Check:
3 
6

4 
6
1 
5 
2
 

1 
24 
2
1 
18 
2
1 
12 
2

1 
30 
2
 

3 
1 
0 
2
3 
1 
0 
2  
6 

4 
7 
2
 
427 
30127m 
301234 
12121212 
3 

1 
4 
2
 
2 2 124 
123 
666 
33 
(|| Print ||) || Print ||
Copyright  by Holt, Rinehart and Winston. 

81 Holt Middle School Math

All rights reserved. 


